log transformation

[mirra]

I am trying to understand the relationship between lognormal and normal distribution.
I understand that a variable transformed into a normal distribution by taking the log of it has a lognormal distribution.
I thought that the pdf of this log transformed variable is , but looking at Wikipedia, this is the pdf of the lognormal distiribution. I am very confused and would really appreciate an explanation.

 

[Dason]

I don't understand what you're confused about

 

[mirra]

I am sorry, my question was not very clear. I make another try:

If one takes the log of a log-normal variable the resulting log-variable is normally distributed.
My question is then, what is the pdf of this log-variable?
Is it log [ ], where is the pdf of a log-normal variable.

I would like to know this because I want to transform a log-normal distribution into a normal distribution to work with it.

 

[mirra]

When taking the log of a lognormally distributed variable (left graph) we get a normally distributed variable (right graph).

The probability density function (PDF) of the left graph is:
What is the PDF of the right graph?

I have read somewhere that the PDF of the right graph is . But I am confused, because this is the PDF of the graph to the left.